A micro macro approach to rubber like materials Part II The micro sphere model of finite rubber viscoelasticity

Date

2005-10-01

Author

Christian, Miehe
Göktepe, Serdar

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

284
views

0
downloads

A micromechanically based non-affine network model for finite rubber elasticity incorporating topological constraints was discussed in Part 1 (2004. J. Mech. Phys. Solids 52, 2617-2660) of this work. In this follow-up contribution we extend the non-affine microsphere model towards the description of time-dependent viscoelastic effects. The viscoelastic network model is constructed by an additive split of the overall response into elastic equilibrium-stress and viscoelastic overstress contributions. The equilibrium response of the network is understood to be related to results obtained from an infinite relaxation process and modeled by our above mentioned elasticity formulation. Inspired by (2004. J. Mech. Phys. Solids 52, 2617-2660), the rate-dependent overstress response is assumed to be driven by two micro-kinematical mechanisms related to the stretch and the area contraction of a tube containing a prototype chain. Firstly, a retraction of fictitiously unconstrained dangling chains is explained by diffusive reptile motions. Secondly, a release of constraint effects due to surrounding chains is modeled by a time-dependence of a tube cross-section area. The latter contribution is considered to be a result of the retraction of forest chains. We outline a distinct micromechanical model for the viscous overstress in terms of the above outlined two micro-kinematic mechanisms and discuss its numerical implementation in context of an affine homogenization procedure of space orientations. The characteristics and modeling capabilities of the proposed micro-sphere model of finite rubber viscoelasticity are reported for a broad spectrum of experimentally-based benchmark simulations. They demonstrate an excellent performance of the model in simulating rate and hystereses effects of rubbery polymers.

Subject Keywords

Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics

URI

https://hdl.handle.net/11511/46810

Journal

Journal Of The Mechanics And Physics Of Solids

DOI

https://doi.org/10.1016/j.jmps.2005.04.006

Collections

Department of Civil Engineering, Article

Suggestions

OpenMETU
Core

A micro-macro approach to rubber-like materials. Part III: The micro-sphere model of anisotropic Mullins-type damage Göktepe, Serdar (Elsevier BV, 2005-10-01) A micromechanically based non-affine network model for finite rubber elasticity and viscoelasticity was discussed in Parts I and II [Miehe, C., Goktepe, S., Lulei, F., 2004. A micro-macro approach to rubber-like materials. Part I: The non-affine micro-sphere model of rubber elasticity. J. Mech. Phys. Solids 52, 2617-2660; Miehe, C., Goktepe, S., 2005. A micro-macro approach to rubber-like materials. Part II: Viscoelasticity model for polymer networks. J. Mech. Phys. Solids, published on-line, doi:10.1016/j....
A variational multiscale constitutive model for nanocrystalline materials Gürses, Ercan (Elsevier BV, 2011-03-01) This paper presents a variational multi-scale constitutive model in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc-material is modeled as a two-phase material consisting of a grain interior phase and a grain boundary effected zone (GBAZ). A rate-independent isotropic porous plasticity model is employed to describe the GBAZ, whereas a crystal-plasticity model which accounts for the transition from partial dislocation to full dislocation m...
Analysis of material instabilities in inelastic solids by incremental energy minimization and relaxation methods: evolving deformation microstructures in finite plasticity MIEHE, CHRISTIAN; LAMBRECHT, MATTHIAS; Gürses, Ercan (Elsevier BV, 2004-12-01) We propose an approach to the definition and analysis of material instabilities in rate-independent standard dissipative solids at finite strains based on finite-step-sized incremental energy minimization principles. The point of departure is a recently developed constitutive minimization principle for standard dissipative materials that optimizes a generalized incremental work function with respect to the internal variables. In an incremental setting at finite time steps this variational problem defines a ...
A NEW METHOD FOR HARMONIC RESPONSE OF NONPROPORTIONALLY DAMPED STRUCTURES USING UNDAMPED MODAL DATA Özgüven, Hasan Nevzat (Elsevier BV, 1987-09-08) A method of calculating the receptances of a non-proportionally damped structure from the undamped modal data and the damping matrix of the system is presented. The method developed is an exact method. It gives exact results when exact undamped receptances are employed in the computation. Inaccuracies are due to the truncations made in the calculation of undamped receptances. Numerical examples, demonstrating the accuracy and speed of the method when truncated receptance series are used are also presented. ...
A NEW FAMILY OF MODE-SUPERPOSITION METHODS FOR RESPONSE CALCULATIONS AKGUN, MA (Elsevier BV, 1993-10-22) A new family of mode-superposition methods for the computation of the forced response of proportionally damped systems with and without rigid body modes is investigated. The method may be considered to be an extension of the mode-acceleration method. It allows response calculations to be done with a very small subset of the modes of the system. Numerical examples are given for systems of order 20 and 40. Execution times and number of modes required for convergence are recorded. The particular order of the m...

Citation Formats

M. Christian and S. Göktepe, “A micro macro approach to rubber like materials Part II The micro sphere model of finite rubber viscoelasticity,” Journal Of The Mechanics And Physics Of Solids, pp. 2231–2258, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46810.